Weight Paint isn't painting smoothly?
I see that you're trying to paint between vertices, you can't, if you want the painting to be more subtle you need to subdivide your object. And of course you also need to use the good brush strength (you can mainly use the Draw brush in Mix or Subtract mode, F to change the brush radius, ShiftF to change its strength, you can also use the Blur brush to smooth).
Weight painting is used to give a value between 0 (blue) and 1 (red) to your vertices, 0 meaning the selected vertex group (in the Vertex Groups list) has 0% influence on this vertex, 1 (red) meaning it has 100% influence on this vertex.
Which doesn't mean that this vertex can't be part of other vertex groups by the way, several groups can have a weight of 1, which means they will equally influence this vertex.
So you can't paint edges or faces, only vertices.
If you open the N panel &gt; Item &gt; Vertex Weight, you can select a vertex and see what group this vertex is part of and how much weight this group has on this vertex:

Also, good thing to know, if you want to paint through, disable the Front Faces Only and Front-face Falloff options and enable Projected: